This invention relates to electronic music production and reproduction and to methods for modifying electronic analogs of sound during the process of amplifying and enhancing the signals generated by a note, and in general to systems having the objective of quickly determining the fundamental frequency of a compound wave which is the sum of multiple frequencies.
There is an irreducible minimum limit to the length of time required to measure the frequency of a sine wave signal to a specified pitch accuracy (e.g., to xc2xc of a semitone). That minimum time is inversely proportional to the frequency of the signal being processed. Keeping pitch accuracy constant, the minimum amount of time required to measure the frequency of a pure sine wave of 82.4 Hz would be eight times longer than the minimum time required to measure the frequency of a pure sine wave of 659.2 Hz. Accordingly, the lag time for measuring and reproducing the fundamental frequencies of low bass notes which are produced by instruments not incorporating keyboards (or other means of revealing the fundamental frequency as a note is sounded) is problematic. For example, when the signals from low bass notes are processed by synthesizers before they are amplified and reproduced, an annoying lag time commonly results.
Throughout this patent, a partial or partial frequency is defined as a definitive energetic frequency band, and harmonics or harmonic frequencies are defined as partials which are generated in accordance with a phenomenon based on an integer relationship such as the division of a mechanical object, e.g., a string, or of an air column, by an integral number of nodes. The relationships between and among the harmonic frequencies generated by many classes of oscillating/vibrating devices, including musical instruments, can be modeled by a function G(n) such that
fn=f1xc3x97G(n)
where fn is the frequency of the nth harmonic, f1 is the fundamental frequency, known as the 1st harmonic, and n is a positive integer which represents the harmonic ranking number. Known examples of such functions are:
fn=f1xc3x97n;
and,
fn=f1xc3x97nxc3x97[1+(n2xe2x88x921)xcex2]xc2xd.
Where xcex2 is a constant, typically 0.004.
A body of knowledge and theory exists regarding the nature and harmonic content of complex wave forms and the relationships between and among the harmonic partials produced both by vibrating objects and by electrical/electronic analogs of such objects. Examples of texts which contribute to this body of knowledge are 1) The Physics of Musical Instruments by Fletcher and Rossing, 2) Tuning, Timbre, Spectrum, Scale by Sethares, and 3) Digital Processing of Speech Signals by Rabiner and Schafer. Also included are knowledge and theory concerning various ways to measure/determine frequency, such as fixed and variable band-pass and band-stop filters, oscillators, resonators, fast Fourier transforms, etc. An overview of this body of knowledge is contained in the Encyclopedia Britannica.
Examples of recent patents which specifically address ways to measure a fundamental frequency are:
U.S. Pat. No. 5,780,759 to Szalay describes a pitch recognition method that uses the interval between zero crossings of a signal as a measure of the period length of the signal. The magnitude of the gradient at the zero crossings is used to select the zero crossings to be evaluated.
U.S. Pat. No. 5,774,836 to Bartkowiak et al. shows an improved vocoder system for estimating pitch in a speech wave form. The method first performs a correlation calculation, then generates an estimate of the fundamental frequency. It then performs error checking to disregard xe2x80x9cerroneousxe2x80x9d pitch estimates. In the process, it searches for higher harmonics of the estimated fundamental frequency.
U.S. Pat. No. 4,429,609 to Warrander shows a device and method which performs an A to D conversion, removes frequency bands outside the area of interest, and performs analysis using zero crossing time data to determine the fundamental. It delays a reference signal by successive amounts corresponding to intervals between zero crossings, and correlates the delayed signal with the reference signal to determine the fundamental.
U.S. Pat. No. 5,210,366 to Sykes, Jr. is a system and method for detecting, separating and recording the individual voices in a musical composition performed by a plurality of instruments. The electrical waveform signal for the multi-voiced musical composition is fed to a waveform signal converter to convert the waveform signal to a frequency spectrum representation. The frequency spectrum representation is fed to a frequency spectrum comparator where it is compared to predetermined stedy-state frequency spectrum representations for a particular musical instrument. Upon detecting the presence of a frequency spectrum representation corresponding to a predetermined steady-state frequency spectrum representation, the detected frequency spectrum representation and measured growth and decay frequency spectrum representations are fed to a waveform envelope comparator and compared to predetermined waveform envelopes, i.e. frequency spectrum representations during the growth, steady-state and transient properties of the detected frequency spectrum representation are recorded and converted to an electrical waveform signal for output as music data for an individual voice.
U.S. Pat. No. 5,536,902 to Serra et al. is a method and apparatus for analyzing and synthesizing a sound by extracting controlling a sound parameter. Analysis data are provided which are indicative of plural components making up an original sound waveform. The analysis data are analysed to obtain a characteristic concerning a predetermined element, and then data indicative of the obtained characteristics is extracted as a sound or musical parameter. The pitch or fundamental frequency is determined by a weighted average of lower order partials.
The present invention is a method to determine harmonics in a compound wave by being performed without knowing or detecting the fundamental frequency. The method includes detecting the higher order partial frequencies of the compoundwave and determining mathematically the harmonic relationship between and among the higher partial frequencies. The fundamental frequency is deduced from the determined harmonic relationship of the detected frequencies and ranking numbers with which they are paired. This can be performed before the fundamental frequency can be measured. Where the compound waves include a plurality set of harmonics, each set is stemming from a different common fundamental frequency, the method is repeated to determine all sets of harmonics in the compound wave.
The present invention is a method to quickly deduce the fundamental frequency of a complex wave form or signal by using the relationships between and among the frequencies of higher harmonics.
The method includes selecting at least two candidate frequencies in the signal. Next, it is determined if the candidate frequencies are a group of legitimate harmonic frequencies having a harmonic relationship. Finally, the fundamental frequency is deduced from the legitimate frequencies.
In one method, relationships between and among detected partial frequencies are compared to comparable relationships that would prevail if all members were legitimate harmonic frequencies. The relationships compared include frequency ratios, differences in frequencies, ratios of those differences, and unique relationships which result from the fact that harmonic frequencies are modeled by a function of a variable which assumes only positive integer values. That integer value is known as the harmonic ranking number. Preferably, the function of an integer variable is fn=f1xc3x97nxc3x97(S)log2n where S is a constant and typically, 1xe2x89xa6Sxe2x89xa61.003 and n is the harmonic ranking number. The value of S, hereafter called the sharping constant, determines the degree to which harmonics become progressively sharper as the value of n increases.
Other relationships which must hold if the candidate partial frequencies are legitimate harmonics stem from the physical characteristics of the vibrating/oscillating object or instrument that is the source of the signal, i.e., the highest and lowest fundamental frequencies it can produce and the highest harmonic frequency it can produce.
Another method for determining legitimate harmonic frequencies and deducing a fundamental frequency includes comparing the group of candidate frequencies to a fundamental frequency and its harmonics to find an acceptable match. One method creates a harmonic multiplier scale on which the values of G(n) are recorded. Those values are the fundamental frequency multipliers for each value of n, i.e., for each harmonic ranking number. Next a like scale is created where the values of candidate partial frequencies can be recorded. After a group of candidate partial frequencies have been detected and recorded on the candidate scale, the two scales are compared, i.e., they are moved with respect to each other to locate acceptable matches of groups of candidate frequencies with groups of harmonic multipliers. Preferably the scales are logarithmic. When a good match is found, then a possible set of ranking numbers for the group of candidate frequencies is determined (or can be read off directly) from the harmonic ranking number scale. Likewise the implied fundamental frequency associated with the group of legitimate partial candidate frequencies can be read off directly. It is the frequency in the candidate frequency scale which corresponds to (lines up with) the xe2x80x9c1xe2x80x9d on the harmonic multiplier scale.
If the function G(n) is different for different frequency registers so that the harmonics in one frequency register are related in ways that are different from the ways they are related in other frequency registers, then different harmonic multiplier scales are generated, one for each of the different frequency registers. Partial frequencies are recorded on the scale appropriate for the frequency register in which they fall and are compared with the harmonic multiplier scale which corresponds to that frequency register.
In another matching method, the candidate frequencies are compared to a plurality of detected measured harmonic frequencies stemming from a plurality of fundamental frequencies. The detected and measured harmonic frequencies are preferably organized into an array where the columns are the harmonic ranking numbers and the rows are the harmonic frequencies organized in fundamental frequency order. When three or more detected partials align sufficiently close to three measured harmonic frequencies in a row of the array, the harmonic ranking numbers and the fundamental are known.
Since the frequencies of the higher harmonics normally can be determined more quickly than the fundamental frequency, and since the calculations to deduce the fundamental frequency can be performed in a very short time, the fundamental frequencies of low bass notes can be deduced well before they can be measured.
Other advantages and novel features of the present invention will become apparent from the following detailed description of the invention when considered in conjunction with the accompanying drawings.